Hi, OP, secondary teacher here (English is my subject). I think it's very rare that schools don't set homework.
I set the following homeworks throughout the academic year:
Year 7 and 8 - 2 homeworks per week. 1 is always reading (I say minimum 45 mins. for Y7 and 1 hr. for Y8 then writing in their reading logs) and the other is a written task taking approx. 30 mins. connected to whatever we're studying.
Year 9 - 1 homework per week, approx. 45 mins. They're expected to read and update reading logs regularly too.
Years 10 and 11 - 2 homeworks per week, approx. 45 mins. each (one for Lang. and one for Lit.)
Sixth form - we suggest 5 hours independent study per week per subject which might be reading, writing their own notes, researching or drafting coursework, researching contextual factors of their set writers or set texts, writing essays, preparing presentations or simply revising.
At my school we have a policy whereby students' homework must be marked by a teacher at least once every two weeks. I tend to mark most if not all homework but other teachers do self or peer assessment on the alternate weeks, (or some tasks might not require "marking" per se e.g. revising for a test, research, making notes, group work towards a presentation or poster, etc.)
I remember reading in the last 6 to 12 months about a school somewhere in the south of England (from memory Brighton maybe?) that didn't set homework but instead had after school clubs where students could work with teacher support. Parents, students and teachers loved it. For some reason the school was more or less forced (I can't remember by whom? Ofsted??) to start setting homework and everyone was very disappointed. (Sorry not to be more specific with details of this case!)
As far as I can remember, the Sutton report found that homework had a marginal positive effect on pupils' progress. (Happy to be wrong on this one, again, relying on ever less reliable memory).